29,537 research outputs found
High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: Sampling Cost via Incident-Field Windowing and Recentering
This paper proposes a frequency/time hybrid integral-equation method for the
time dependent wave equation in two and three-dimensional spatial domains.
Relying on Fourier Transformation in time, the method utilizes a fixed
(time-independent) number of frequency-domain integral-equation solutions to
evaluate, with superalgebraically-small errors, time domain solutions for
arbitrarily long times. The approach relies on two main elements, namely, 1) A
smooth time-windowing methodology that enables accurate band-limited
representations for arbitrarily-long time signals, and 2) A novel Fourier
transform approach which, in a time-parallel manner and without causing
spurious periodicity effects, delivers numerically dispersionless
spectrally-accurate solutions. A similar hybrid technique can be obtained on
the basis of Laplace transforms instead of Fourier transforms, but we do not
consider the Laplace-based method in the present contribution. The algorithm
can handle dispersive media, it can tackle complex physical structures, it
enables parallelization in time in a straightforward manner, and it allows for
time leaping---that is, solution sampling at any given time at
-bounded sampling cost, for arbitrarily large values of ,
and without requirement of evaluation of the solution at intermediate times.
The proposed frequency-time hybridization strategy, which generalizes to any
linear partial differential equation in the time domain for which
frequency-domain solutions can be obtained (including e.g. the time-domain
Maxwell equations), and which is applicable in a wide range of scientific and
engineering contexts, provides significant advantages over other available
alternatives such as volumetric discretization, time-domain integral equations,
and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now
including direct comparisons to existing CQ and TDIE solver implementations)
(Part I of II
Wavelet transforms and their applications to MHD and plasma turbulence: a review
Wavelet analysis and compression tools are reviewed and different
applications to study MHD and plasma turbulence are presented. We introduce the
continuous and the orthogonal wavelet transform and detail several statistical
diagnostics based on the wavelet coefficients. We then show how to extract
coherent structures out of fully developed turbulent flows using wavelet-based
denoising. Finally some multiscale numerical simulation schemes using wavelets
are described. Several examples for analyzing, compressing and computing one,
two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201
Velocity Field of Compressible MHD Turbulence: Wavelet Decomposition and Mode Scalings
We study compressible MHD turbulence, which holds key to many astrophysical
processes, including star formation and cosmic ray propagation. To account for
the variations of the magnetic field in the strongly turbulent fluid we use
wavelet decomposition of the turbulent velocity field into Alfven, slow and
fast modes, which presents an extension of the Cho & Lazarian (2003)
decomposition approach based on Fourier transforms. The wavelets allow to
follow the variations of the local direction of magnetic field and therefore
improve the quality of the decomposition compared to the Fourier transforms
which are done in the mean field reference frame. For each resulting component
we calculate spectra and two-point statistics such as longitudinal and
transverse structure functions, as well as, higher order intermittency
statistics. In addition, we perform the Helmholtz-Hodge decomposition of the
velocity field into the incompressible and compressible parts and analyze these
components. We find that the turbulence intermittency is different for
different components and we show that the intermittency statistics depend on
whether the phenomenon was studied in the global reference frame related to the
mean magnetic field or it was studied in the frame defined by the local
magnetic field. The dependencies of the measures we obtained are different for
different components of velocity, for instance, we show that while the Alfven
mode intermittency changes marginally with the Mach number the intermittency of
the fast mode is substantially affected by the change.Comment: 16 pages, 9 figures, 2 table
Semi-analytical and numerical methods for computing transient waves in 2D acoustic / poroelastic stratified media
Wave propagation in a stratified fluid / porous medium is studied here using
analytical and numerical methods. The semi-analytical method is based on an
exact stiffness matrix method coupled with a matrix conditioning procedure,
preventing the occurrence of poorly conditioned numerical systems. Special
attention is paid to calculating the Fourier integrals. The numerical method is
based on a high order finite-difference time-domain scheme. Mesh refinement is
applied near the interfaces to discretize the slow compressional diffusive wave
predicted by Biot's theory. Lastly, an immersed interface method is used to
discretize the boundary conditions. The numerical benchmarks are based on
realistic soil parameters and on various degrees of hydraulic contact at the
fluid / porous boundary. The time evolution of the acoustic pressure and the
porous velocity is plotted in the case of one and four interfaces. The
excellent level of agreement found to exist between the two approaches confirms
the validity of both methods, which cross-checks them and provides useful tools
for future researches.Comment: Wave Motion (2012) XX
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